Prove Z[sqrt(d)] is not a UFD when d=1 mod 4

Let $\displaystyle d \equiv 1 \pmod{4}$ be a square-free integer with $\displaystyle d \neq 1$. By considering the factorisation of $\displaystyle d-1$, show that the ring $\displaystyle \mathbb{Z}[\sqrt{d}]$ is never a Unique Factorisation Domain.

Let $\displaystyle d \equiv 1 \pmod{4}$ be a square-free integer with $\displaystyle d \neq 1$. By considering the factorisation of $\displaystyle d-1$, show that the ring $\displaystyle \mathbb{Z}[\sqrt{d}]$ is never a Unique Factorisation Domain.